html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cos

 http://functions.wolfram.com/01.07.21.2636.01

 Input Form

 Integrate[E^(b Sqrt[z]) Sin[b Sqrt[z]]^m Cos[c Sqrt[z]]^v, z] == (1/b^2) (2^(1 - m - v) E^(b Sqrt[z]) (-1 + b Sqrt[z]) Binomial[m, m/2] Binomial[v, v/2] (1 - Mod[m, 2]) (1 - Mod[v, 2])) + 2^(1 - m - v) Binomial[v, v/2] (1 - Mod[v, 2]) Sum[(-1)^k ((E^((I m Pi)/2 + (b - I b (-2 k + m)) Sqrt[z]) (-1 + (b - I b (-2 k + m)) Sqrt[z]))/(b - I b (-2 k + m))^2 + (E^((-(1/2)) I m Pi + (b + I b (-2 k + m)) Sqrt[z]) (-1 + (b + I b (-2 k + m)) Sqrt[z]))/(b + I b (-2 k + m))^2) Binomial[m, k], {k, 0, Floor[(1/2) (-1 + m)]}] + 2^(1 - m - v) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[((E^((b - I c (-2 s + v)) Sqrt[z]) (-1 + (b - I c (-2 s + v)) Sqrt[z]))/(b - I c (-2 s + v))^2 + (E^((b + I c (-2 s + v)) Sqrt[z]) (-1 + (b + I c (-2 s + v)) Sqrt[z]))/ (b + I c (-2 s + v))^2) Binomial[v, s], {s, 0, Floor[(1/2) (-1 + v)]}] + 2^(1 - m - v) Sum[(-1)^k Binomial[m, k] Sum[((E^((I m Pi)/2 + (b - I b (-2 k + m) - I c (-2 s + v)) Sqrt[z]) (-1 + (b - I b (-2 k + m) - I c (-2 s + v)) Sqrt[z]))/ (b - I b (-2 k + m) - I c (-2 s + v))^2 + (E^((-(1/2)) I m Pi + (b + I b (-2 k + m) - I c (-2 s + v)) Sqrt[z]) (-1 + (b + I b (-2 k + m) - I c (-2 s + v)) Sqrt[z]))/ (b + I b (-2 k + m) - I c (-2 s + v))^2 + (E^((I m Pi)/2 + (b - I b (-2 k + m) + I c (-2 s + v)) Sqrt[z]) (-1 + (b - I b (-2 k + m) + I c (-2 s + v)) Sqrt[z]))/ (b - I b (-2 k + m) + I c (-2 s + v))^2 + (E^((-(1/2)) I m Pi + (b + I b (-2 k + m) + I c (-2 s + v)) Sqrt[z]) (-1 + (b + I b (-2 k + m) + I c (-2 s + v)) Sqrt[z]))/ (b + I b (-2 k + m) + I c (-2 s + v))^2) Binomial[v, s], {s, 0, Floor[(1/2) (-1 + v)]}], {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0 && Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 b z sin m ( b z ) cos v ( c z ) z 2 - m - v + 1 b z ( b z - 1 ) ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) b 2 + 2 - m - v + 1 ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) k = 0 m - 1 2 ( - 1 ) k ( ( ( m - 2 k ) b + b ) z - m π 2 ( ( ( m - 2 k ) b + b ) z - 1 ) ( ( m - 2 k ) b + b ) 2 + π m 2 + ( b - b ( m - 2 k ) ) z ( ( b - b ( m - 2 k ) ) z - 1 ) ( b - b ( m - 2 k ) ) 2 ) ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] + 2 - m - v + 1 ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) s = 0 v - 1 2 ( ( b + c ( v - 2 s ) ) z ( ( b + c ( v - 2 s ) ) z - 1 ) ( b + c ( v - 2 s ) ) 2 + ( b - c ( v - 2 s ) ) z ( ( b - c ( v - 2 s ) ) z - 1 ) ( b - c ( v - 2 s ) ) 2 ) ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] + 2 - m - v + 1 k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] s = 0 v - 1 2 ( ( ( ( m - 2 k ) b + b + c ( v - 2 s ) ) z - m π 2 ( ( ( m - 2 k ) b + b + c ( v - 2 s ) ) z - 1 ) ) / ( ( m - 2 k ) b + b + c ( v - 2 s ) ) 2 + ( π m 2 + ( - ( m - 2 k ) b + b + c ( v - 2 s ) ) z ( ( - ( m - 2 k ) b + b + c ( v - 2 s ) ) z - 1 ) ) / ( - ( m - 2 k ) b + b + c ( v - 2 s ) ) 2 + ( ( ( m - 2 k ) b + b - c ( v - 2 s ) ) z - m π 2 ( ( ( m - 2 k ) b + b - c ( v - 2 s ) ) z - 1 ) ) / ( ( m - 2 k ) b + b - c ( v - 2 s ) ) 2 + ( π m 2 + ( - ( m - 2 k ) b + b - c ( v - 2 s ) ) z ( ( - ( m - 2 k ) b + b - c ( v - 2 s ) ) z - 1 ) ) / ( - ( m - 2 k ) b + b - c ( v - 2 s ) ) 2 ) ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] /; m + v + Condition z b z 1 2 b z 1 2 m c z 1 2 v 2 -1 m -1 v 1 b z 1 2 b z 1 2 -1 Binomial m m 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 b 2 -1 2 -1 m -1 v 1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 -1 k m -1 2 k b b z 1 2 -1 m 2 -1 m -1 2 k b b z 1 2 -1 m -1 2 k b b 2 -1 m 2 -1 b -1 b m -1 2 k z 1 2 b -1 b m -1 2 k z 1 2 -1 b -1 b m -1 2 k 2 -1 Binomial m k 2 -1 m -1 v 1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 s 0 v -1 2 -1 b c v -1 2 s z 1 2 b c v -1 2 s z 1 2 -1 b c v -1 2 s 2 -1 b -1 c v -1 2 s z 1 2 b -1 c v -1 2 s z 1 2 -1 b -1 c v -1 2 s 2 -1 Binomial v s 2 -1 m -1 v 1 k 0 m -1 2 -1 -1 k Binomial m k s 0 v -1 2 -1 m -1 2 k b b c v -1 2 s z 1 2 -1 m 2 -1 m -1 2 k b b c v -1 2 s z 1 2 -1 m -1 2 k b b c v -1 2 s 2 -1 m 2 -1 -1 m -1 2 k b b c v -1 2 s z 1 2 -1 m -1 2 k b b c v -1 2 s z 1 2 -1 -1 m -1 2 k b b c v -1 2 s 2 -1 m -1 2 k b b -1 c v -1 2 s z 1 2 -1 m 2 -1 m -1 2 k b b -1 c v -1 2 s z 1 2 -1 m -1 2 k b b -1 c v -1 2 s 2 -1 m 2 -1 -1 m -1 2 k b b -1 c v -1 2 s z 1 2 -1 m -1 2 k b b -1 c v -1 2 s z 1 2 -1 -1 m -1 2 k b b -1 c v -1 2 s 2 -1 Binomial v s m SuperPlus v SuperPlus [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2002-12-18